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GATE 2021 CE (CE2) – Question 58

Hydrology · Hydrologic cycle, precipitation, evaporation, evapo-transpiration, infiltration · 2 marks · Numerical answer

A rainfall hyetograph has seven half-hour intensities 12,4.5,15,14,4,7.5,3 mm/h. Total rainfall is 3 cm and direct runoff is 1.6 cm. Find φ-index in mm/h to one decimal.

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Correct answer: 4.2 to 4.2

Explanation

Only intervals with intensity above φ produce excess rainfall. Assuming 4<φ<4.5 excludes the 4 and 3 mm/h intervals. Then $16=0.5[(12+4.5+15+14+7.5)-5\phi]$, giving **φ=4.2 mm/h**. This satisfies the assumed interval and exactly reproduces the 16 mm runoff.